Geometric Mean Decomposition for MIMO Transceiver Design

In recent years, considerable attention has been paid to the joint optimal transceiver design for multi-input multi-output (MIMO) communication systems. The singular value decomposition (SVD), which decomposes a MIMO channel into multiple parallel subchannels, and water filling can be used to achieve the channel capacity. However, due to the very different SNRs of the subchannels, this apparently simple scheme requires complicated bit allocation to match the subchannel capacity and achieve a prescribed BER. Two most typical linear precoder designs are MTM which minimizes the trace of the MSE matrix of the estimate of the information symbol and MMD which minimizes the maximum diagonal elements of MSE matrix. However, our analysis shows that the MTM transceiver suffers from capacity loss due to the information theoretically nonoptimal power. The MMD transceiver suffers from additional capacity loss because it makes the MSE matrix nondiagonal. Hence, there is an apparently inevitable tradeoff between the information rate and BER performance if the same symbol constellation is used in the different subchannels.

This motivates us to propose a novel transceiver design based on the geometric mean decomposition (GMD) [11] and clarify that there is not necessarily a tradeoff between BER performance and channel capacity. By combining GMD with either the conventional VBLAST decoder, which is in fact a generalized decision feedback equalizer (GDFE), or the more recent zero-forcing dirty paper precoder (ZFDP), our scheme decomposes an MIMO channel into multiple identical parallel subchannels. This desirable property can bring about much convenience in coding/decoding and modulation/demodulation processes. Moreover, we prove that our scheme is asymptotically optimal for (moderately) high SNR in terms of both channel throughput and BER performance. Hence, the GMD scheme does not make tradeoffs between the throughput and the BER performance. Instead, it attempts to get the best of the both worlds simultaneously. Furthermore, we have shown that the GMD scheme can be applied without the need to use training symbols for channel estimation if combined with subspace tracking techniques. We have also considered the issue of subchannel selection when some of the subchannels are too poor to be useful. The GMD scheme can also be combined with OFDM for ISI suppression. Both the theoretical analyses and empirical simulations have been provided to validate the effectiveness of our approaches.

One recent application of our GMD scheme is to apply it to the capacity-approaching transceiver design for the asymmetric UWB links, which has been proved to have an equivalent MIMO system I/O relationship. Analysis and simulations in [10] show that the GMD-based transceiver designs are feasible for asymmetric UWB designs and their integration is optimum in terms of both BER performance and throughput (see Fig. 3 and Fig. 4).

Fig. 3. BER performance of asymmetric UWB links.

Fig. 4. Throughput comparison.

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This material is based upon work supported by the National Science Foundation under Grant No. 0621879. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.